Engines combust a mixture of air and fuel to drive pistons and generate drive torque. Exhaust gas resulting from combustion is treated by an exhaust system before being released into the atmosphere. Example components of the exhaust system include catalysts and particulate matter (PM) filters. Catalysts chemically convert portions of the exhaust gas, and PM filters trap PM in the exhaust gas. Once a PM filter is has reached a maximum storage capacity, it is regenerated by burning the trapped PM at a high temperature. The stress on the PM filter could cause it to crack, which could decrease exhaust system performance and thus increases emissions, Conventional diagnostic systems for a cracked PM filter utilize a PM or particulate number (PN) sensor. These sensors, however, are expensive and thus increase vehicle costs. Therefore, while such diagnostic systems work for their intended purpose, there remains a need for improvement in the relevant art.